NEW YORK, May 2 (Reuters) - Yields on U.S. 30-year bonds dropped to their lowest in more than 10 months on Friday, falling for a fourth straight session, as concerns about Russia and Ukraine overshadowed an upbeat U.S. employment report.

U.S. 30-year bond yields fell as low as 3.34 percent, their weakest level since June 19, 2013, after hitting session highs on the jobs number. U.S. 10-year note yields, meanwhile, slid to 2.57 percent, a three-month trough, on news about Russia and Ukraine.

Reports that Russia had called for a meeting of the United Nations Security Council over a Ukrainian army operation in the southeastern city of Slaviansk drove a rally in Treasuries.

The report came after Treasuries sold off as the U.S. nonfarm payrolls figure came in higher than expected.

“Shortly after this morning’s jobs report, it looked like the world might be returning to an ‘old fashioned’ bond market where macroeconomic fundamentals rule,” said Jonathan Lewis, managing principal and chief investment officer, at Samson Capital Advisors, in New York.

“Then the spotlight turned to Ukraine, a worsening geopolitical environment, and suddenly the jobs report was forgotten. Stocks are down, longer maturity treasuries have turned from a loss to a gain, and gold is having its best day in some time.”

In afternoon trading, the benchmark 10-year U.S. Treasury note was up 5/32 on the day to yield 2.58 percent, compared with 2.62 percent late on Thursday. Yields hit session highs of 2.70 percent following the jobs number.

Data showed that U.S. nonfarm payrolls surged by 288,000 in April, the most since January 2012, while the jobless rate dropped to a 5-1/2-year low of 6.3 percent. The headline jobs figure handily beat Wall Street’s expectations for an increase of just 210,000.

Still, some economists took issue with the unemployment rate, which included a decline in the labor force by 806,000, the fourth-largest since data recording started in 1948.

“The market perceives the unemployment numbers as good on quantity, but bad on quality,” said Guy Lebas, chief fixed income strategist, at Janney Montgomery Scott in Philadelphia.

“The five-year ... is a better response to the unemployment rate rather than the 10- or 30-year because that’s going to embody the timing of the Fed rate hikes a little bit more effectively,” he said.

Lebas said the five-year sold off, but yields were not far from lows.

The five-year note was last down 3/32, yielding 1.72 percent, from 1.67 percent late Thursday. The yield hit the day’s high of 1.76 percent after the payrolls data was released, while the low was 1.65 percent.

The 5-year note has led a selloff over the past few sessions.

“I still think overall there is a tremendous amount of shorts in the market,” said Tom di Galoma, head of fixed-income at ED&F Man in New York.

“We’ve seen buyers on dips.cI think probably this is going to continue with this thing in Ukraine and Russia. It’s just a continuation of this flight-to-quality bid.” (Editing by Diane Craft)